Find the 15th term of the A.P. 21, 16,11,6……….

Answer

To find the 15th term of the arithmetic progression (A.P.) given as 21, 16, 11, 6, we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d).
- The first term \( a \) is the first number in the sequence, which is \( 21 \).
- The common difference \( d \) can be calculated by subtracting the first term from the second term:
\[ d = a_2 - a_1 = 16 - 21 = -5 \]

### Step 2: Use the formula for the nth term of an A.P.
The formula for the nth term of an A.P. is given by:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a_n \) is the nth term,
- \( a \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.

### Step 3: Substitute the values into the formula.
We want to find the 15th term (\( n = 15 \)):
\[ a_{15} = a + (15 - 1) \cdot d \]
Substituting the known values:
\[ a_{15} = 21 + (15 - 1) \cdot (-5) \]
\[ a_{15} = 21 + 14 \cdot (-5) \]

### Step 4: Calculate the value.
Now, calculate \( 14 \cdot (-5) \):
\[ 14 \cdot (-5) = -70 \]
Now substitute this back into the equation:
\[ a_{15} = 21 - 70 \]
\[ a_{15} = -49 \]

### Final Answer:
The 15th term of the A.P. is \( -49 \).

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